Use the Add-a-Plotter wizard (PLOTTERMANAGER) to add a raster "printer" - eg. for the TIFF format: use This Computer, select Raster File Formats (as Manufacturer) and under Model select TIFF (or PNG, JPG...).
Raster image size is unitless (in pixels, not inches or mm) - to increase resolution of the raster file (in pixels) set a "larger paper size". You can create a custom "paper" size for this "printer" - increase this paper size to achieve higher resolution (more pixels in the resulting raster file). The DPI (dots-per-inch) value is usually fixed (e.g. 100 dpi) so to get 2000 pixel resolution you will have to set 2000/100 = 20 inches page size. In higher AutoCAD versions you can use directly pixels so you don't need to recalculate page size values.
Under Device settings you can set the color depth (for color formats) - fewer colors means smaller files.
You can also export DWGs to other raster formats - CALS, JPG/JPEG, BMP, PNG, TGA, PCX. All standard print settings (line weights, plot styles...) will apply. And you can also use standard AutoCAD batch plot operations for these exports.
Please note that you cannot control resolution/quality for the direct JPGOUT, PNGOUT and similar commands.